On the Donnell's equations in the creep range

Abstract

Abstract This paper is concerned with assessing the accuracy of Donnell's approximation when employed in the creep analysis of a class of circular cylindrical shells. Basic formulation of a general method describing the creep behaviour of two-dimensional cylindrical shells is first presented. The terms affected by Donnell's approximation are then pointed out. The solution of governing equations is obtained through coupling the ‘extended Newton's method’ and finite difference technique in an iterative procedure. A number of examples having geometries falling within the shallow shell definition, around the limit, and beyond the range of applicability, are solved using both theories. It has been noted that the parameter α, representing the shell geometry, has a pronounced effect on the accuracy of Donnell's simplification. As α increases the deviation between the two theories decreases. It is concluded that for the class of circular cylindrical shells considered herein Donnell's approximations yield accurate results for creep analysis, particularly for higher values of creep exponent n . Of course, employing Donnell's approximations results in simpler formulation and a reduction in computational time.